SUPPLEMENTAL MATERIAL
Sequentially-pulsed fluid delivery to establish soluble gradients
within a scalable microfluidic chamber array
Edward S. Park,1 Michael A. DiFeo,1 Jacqueline M. Rand,1 Matthew M. Crane2,3
and Hang Lu1,2,3,a)
1
School of Chemical & Biomolecular Engineering, Georgia Institute of Technology,
Atlanta, Georgia 30332, USA
2
The Parker H. Petit Institute of Bioengineering and Bioscience, Georgia Institute of
Technology and Emory University, Atlanta, Georgia 30332, USA
3
Interdisciplinary Program of Bioengineering, Georgia Institute of Technology and
Emory University, Atlanta, Georgia 30332, USA
REVIEW OF FLOW-BASED AND DIFFUSION-BASED DESIGNS
For brief review, flow-based systems rely upon diffusion among multiple parallel flow
streams to produce gradients.1-7 The flow streams are loaded with different signal
concentrations, which is achieved by an upstream mixing network that splits and recombines
flow streams over multiple generations. When the streams meet in the main chamber, lateral
diffusion between them produces a signal gradient perpendicular to the direction of flow. The
flow-based concept is an elegant and seminal invention in microfluidic chemotaxis assays,3
distinguished by the superb stability and predictability of its gradients. Though, flow-based
systems face a number of limitations, depending on study requirements. First, cells may exhibit
unintended responses to shear stresses caused by the flow streams that pass directly over them.8
Second, diffusion between flow streams causes the slope of the gradient to decrease with each
downstream location in the chamber. This limits the number of replicate conditions/locations
available per device (subject to flow rate and the sensitivity of cells to variances in gradient).
Furthermore, it is difficult to create high-density arrays of chambers presenting identical
gradients in flow-based systems. The difficulty arises from the spatially changing gradient,
which limits downstream arraying of chambers, as well as from the upstream mixing network,
which requires considerable on-chip footprint and can only feed into a single chamber at a time.
Consequently, flow-based systems are not amenable to the construction of in-line or 2dimensional chamber arrays that are desirable for high-throughput screening applications.
In contrast, diffusion-based designs produce a gradient by way of diffusion from a source to a
sink across a central chamber.9-17 The source and sink are either flow channels or reservoirs and
are loaded with high and low signal concentrations, respectively. The defining features of a
diffusion-based system are typically porous barriers with high fluidic resistance, which separate
the chamber from the source/sink. The barriers shield the chamber from convection; therefore,
flow-induced shear stresses are minimized, mass transport becomes diffusion-dominated, and at
steady-state, a gradient is established. Diffusion-based systems have been developed using
a)
Author to whom correspondence should be addressed. Electronic mail: hang.lu@chbe.gatech.edu
1
barriers that take a variety of forms, including microcapillary channels (or narrow gaps),10, 16, 18
membranes,9, 11, 13, 15, 17, 19 hydrogels,12 and packed microparticles.20
Diffusion-based systems combine the benefits of a low shear microenvironment and a stable
gradient. However, such systems are limited in the following respects. For example, the high
fluidic resistance of the barriers can reduce diffusion speeds and restrict the range of background
concentrations the gradient can span within the chamber. Ranges that span roughly 0.35 to 0.70
normalized concentration have been reported for microcapillary-based16 and hydrogel-based12
systems, while the balance of concentrations occurs within the barriers. In addition, the barriers
of are often made of different materials/components than the bulk of the device. The
construction of such hybrid material systems typically requires multiple alignment steps and
interfacing of rigid and soft materials, which complicates fabrication.
FURTHER RESULTS AND DISCUSSION
A. Flow rates and pulsing sequences used for gradient generation
It is important to note that the flow rates mentioned above (i.e. 0.25 and 2.5 L/min) are not
chosen to model any particular physiological condition, since the flows do not cross through the
main area of the chamber where cells reside. Therefore, the flow rate is chosen based upon the
profile shape (curved vs. linear) that one desires. Also, the flow rate is chosen based upon
experimental practicalities, where the upper limit is defined by the necessity to make sure the
syringes are not emptied before the experiment is complete, while the lower limit is defined by
the need for flow to be fast enough to complete a full volume change (replenishment) in the side
channels next to the chambers within the time given for the flow pulse.
Regarding the pulsing sequence, we first consider the total cycle time, which is approximated
as the time between pulses (replenishments), provided that the pulses are brief. The total cycle
time can thus be taken to represent the fully stagnant time period during which the concentration
at the source side decays to an arbitrarily set threshold before it is replenished again. In this
work, the threshold is set at 95% of the source concentration. Decay behavior can be estimated
by assuming the case of diffusion between two semi-infinite slabs, when diffusion has
progressed to the point where the concentration profile is nearly linear within a distance that is
the width of the chamber (1200 µm). The equation for interdiffusion between two semi-infinite
slabs is represented as:
c ( x, t ) 
c1  c2   c1  c2  erf 
2
x 
 ,

 2 Dt 
2
(2)
where c1 is 1, c2 is 0, and D ranges from 1×10-10 m2/s to 1×10-9 m2/s (estimates of D for proteins
to small molecules in water, respectively). Profiles are evaluated at time t = 6 and 9 min to
determine decay at x = -600 µm (half the width of the chamber). Depending on the species, such
an estimate shows a decay of 2% to 5% after 3 min for proteins and small molecules,
respectively. For dextran (70,000 MW), the observed decay at the source side is roughly 3%
after 3 min, and is therefore consistent with the estimate. Thus, 3 min is established as the cycle
time to maintain concentrations above the threshold on the source side. If the cycle time is
increased to significantly greater than 3 min, one could imagine the concentration profile
2
exhibiting a “see-saw” effect, where the slope varies in time (assuming relatively brief pulse
times).
The pulsing sequence presents a large parameter space to explore, where the left pulse, right
pulse, and total cycle time can be varied, as well as the relative positions of the pulses within
each cycle. To narrow the parameter space, we fix the total cycle time to 3 min when
characterizing the gradient. We vary the pulse times to determine their effect on the curvature of
the steady-state concentration profile (Fig. 2, main article). One should note that the extent to
which one can shorten the pulse time is limited to the time required for a complete volume
change in the side channels. For this design, the minimum time is 10 s at a flow rate of 0.25
µL/min, which is used in experiments as shown in Fig. 2(a) and (c).
B. Potential limitations of approach and topics of further investigation
As mentioned earlier, there is a potential for the formation of additional gradients consisting
of nutrients or secreted molecules due to cellular metabolism, respiration or signalling. These
gradients could confound the ability to clearly differentiate cellular responses due to the applied
gradient (from the device) and gradients due to cellular processes. For small molecules, the
emergence of confounding gradients is unlikely due to their rapid time scales for diffusion.
Finite element models of O2 and glucose transport support such a position (see section on
nutrient transport models and Fig. 15 in Suppl. Material). However, for large molecules (i.e.
proteins) with low diffusivities, confounding gradients are a possibility, and such gradients could
indeed cause the behaviour observed in preliminary cell experiments, where cells migrate toward
both sides of the chamber in the absence of a device-applied gradient. Secreted autocrine or
paracrine signals could be the source of such gradients.21-22 Additional effects could cause the
creation of confounding gradients, such as adsorption to/desorption from chamber surfaces of
secreted molecules. Since the medium on the sides of the chambers is fully replenished on each
flow pulse, the significance of any adsorption/desorption effects would depend on the diffusion
speed of the molecules in question between the middle and side of the chambers.
One way to reduce the likelihood of confounding gradients is to design the cell loading
channels so they more uniformly distribute cells throughout the chamber. Currently, the loading
channels are closely spaced, which causes cells to be clustered in the middle of the chamber
when loaded. A more uniform distribution can be achieved by increasing the spacing between
the loading channels or by adding more of them. A more uniform distribution of cells would
create a more uniform distribution of potentially confounding signals (assuming the signal is
secreted at an adequate rate). Only at the very sides of the chamber would there be a steep
gradient, and such a region would be excluded from analysis. Another strategy to reduce the
potential for confounding gradients is to reduce the width of the chamber, which decreases the
diffusion length. Whether secreted or consumed, the potentially confounding signal would be
limited in concentration due to diffusion out of the chamber, and any resulting gradient would be
minimized.
One topic that is not investigated in this work is the effect of asymmetric pulsing sequences
on cellular response. In preliminary cell experiments, an asymmetric pulsing sequence is utilized
to generate an exponentially-shaped concentration profile, where the replenishment time on the
right side of the chamber is 16 times that of the left side (as shown in Fig. 2(d)). This pulsing
sequence is used during no-gradient and gradient conditions. If the asymmetric pulsing sequence
introduces corresponding asymmetries in cellular response, one could expect differential
3
responses from cells from the left to the right side of the chamber in the absence of an applied
gradient. Morphological and migrational readouts (i.e. area, circularity, speed) from preliminary
experiments do not indicate obvious differences across the chamber, with the possible exception
of circularity (see Fig. 13, stage 1). However, such observations are not conclusive. A more
complete study is required, utilizing higher-resolution binning (more sections in chamber) and
other markers or measures (e.g. fluorescently-labelled intracellular signals) to determine if
asymmetric responses indeed occur.
As previously mentioned, the pulsing sequence presents a large parameter space to explore,
where the left pulse, right pulse, and total cycle time can be varied. Also, the relative positions
of the pulses within each cycle can be varied. This study investigated differences in
concentration gradient as a result of changes in the left and right pulses within a fixed cycle time
of 3 min. However, the parameter space is virtually infinite, and a more complete scan of such
parameters is required to illuminate where broad gradient shape controllability resides in the
space. Such work is essential to mature the technology.
CAD LAYOUT OF DEVICE
FIG. 7. CAD layout of chamber array device. Blue (top) layer includes flow channels. Black (lower) layer includes
chambers and pressure (control) lines for integrated valves. Light blue features are through -holes (middle layer). Full
labeling of features/channels found in Fig. 4 (main article). Device footprint approximately 24×24 mm. Scale bar 1 mm.
4
FABRICATION PROCESS – ALL-PDMS, SINGLE ALIGNMENT STEP
FIG. 8. Device fabrication process with single alignment step. Figure adopted from Park et al.23 PDMS devices are
fabricated using soft lithography, thermal bonding, and compression-molding. Illustration not to scale.
CHAMBER-TO-CHAMBER GRADIENT COMPARISONS
Realizing chambers that generate identical gradients is an important design goal when scaling
to arrays, since identical gradients in all chambers enhances the array’s replication (and hence
parallelization) potential. In practice, some variation inevitably exists, and measuring such
variation is necessary to evaluate design robustness.
Figure 9 plots the concentration profiles of six chambers in a device. The profiles show
similarity, and variation is shown in standard deviations (Fig. 9(b)). A possible cause of
chamber-to-chamber variation is obstructions in the upstream or downstream flow channels
feeding the chambers, which could be caused by small fabrication defects (misalignments
between layers or asymmetries) or particles that flow into the devices and become lodged in the
flow path. Such events could cause the flow rate to deviate from the intended target rate, making
the flow rates on each side of chambers different, leading to shifting or bending profiles. In
addition, measurement errors may contribute to the variation, such as fluorescent light source
fluctuations and camera noise. Also, inexact alignment of images used for intensity
5
normalization (full bright and full dark) relative to experimental images could cause
registration/shift errors.
FIG. 9. Chamber-to-chamber comparison of concentration profiles. (a) Profiles from 6 chambers in a representative device show
similar shape and near overlap. (b) Mean and standard deviation (SD) for 6 chambers at 12 selected locations. Mean value at
each location is the average across 6 devices characterized at the experimental condition; SD at each location is the mean SD
(chamber-to-chamber) for the 6 devices. Profiles are measured at steady-state at following experimental conditions: 2.5 L/min
flow rate and unequal/asymmetric pulsing schedule (as in Fig. 2(d)). Note: Normalized concentration does not reach unity
because the profiles do not span the full length the chamber in the x-direction.
TIME-TO-STEADY-STATE (RISE TIME) FOR GRADIENTS
The results suggest that the flow rate of delivery pulses has an effect on the rise time; higher
flow rates are shown to decrease the rise time. The rise times are measured using dextran of 70
kDa molecular weight, which is chosen as a representative molecular weight for large
biomolecules. However, external signaling proteins vary significantly in their molecular
weights; for example, epidermal growth factor (EGF) is ~6 kDa, while platelet-derived growth
factor (PDGF) is ~25 kDa, and fibronectin is ~440 kDa. According to the Stokes-Einstein
relationship and assuming that proteins are spherical (simplifying assumption), the diffusion
coefficient is inversely proportional to the cubed root of molecular weight. Taking EGF as an
example, its rise time would be less than half that of the 70 kDa dextran, assuming transport is
purely diffusive. For small molecules, the rise time would be much faster (on the order of
minutes).24 Therefore, the rise times reported in this work are solely demonstrative, as they will
vary depending on the size of the signal of interest. Figure 10 plots the rise characteristics for 70
kDa dextran at different flow rates and pulsing schedules.
6
FIG. 10. Rise of dextran (70 kDa) concentration plotted at two different flow rates and flow pulsing schedules. The higher flow
rate results in a more rapid rise. (a) Times to 80% of steady-state with the equal flow pulses are ~150 min and ~300 min for 2.5
L/min (high) and 0.25 L/min (low), respectively. (b) Unequal pulsing schedule, as tested, also results in a faster rise time.
Times to 80% of steady-state with unequal pulsing schedule for high and low flow rates are ~100 min and ~220 min,
respectively. Fluorescence intensities measured from the center of the chamber. Scale bar is 200 µm.
EXPERIMENTAL SETUP – DEVICE MOUNTED TO MICROSCOPE STAGE WITH
PDMS ENCLOSURE
For experiments, the device is mounted to an inverted microscope with a motorized x-y
stage, which translate through a 6-position circuit to image each chamber in the array. The
device is covered by an optically transparent enclosure (made of PDMS) into which is fed with
humidified air to prevent gas bubble nucleation in the device (Fig. 11). Earlier experiments
without the PDMS enclosure resulted in evaporation and gas bubble nucleation throughout
devices. Most problematically, gas bubbles that formed within chambers would slowly expand
as the experiment progressed, disrupting the gradient and killing cells. Use of the PDMS
enclosure shields the device from direct convection from the heating fan (which maintains the
temperature at 37 °C). Also, humidified air, which is bubbled through a column of water, is
flowed into the enclosure and surrounds the device. This approach eliminated evaporation and
bubble formation.
7
FIG. 11. Setup for cell experiments. Device is mounted to motorized x-y stage on inverted microscope. Flow and pressure tubes
enter device through stainless steel L-shaped pins. Humidified air is flowed into a transparent PDMS enclosure (large PDMS
slabs) around the device to prevent bubble nucleation in the array. Heating fan (not shown) maintains 37 C temperature.
FURTHER DETAILS REGARDING IMAGE PROCESSING, CELL TRACKING, AND
DATA ANALYSIS
Cells are segmented in each image from their respective backgrounds for morphological and
tracking analysis. We apply a heuristic involving image registration, image division, flattening,
and cell segmentation through the use of MATLAB (The MathWorks Inc., Natick, MA, USA)
and Image-Pro 6.1 (Media Cybernetics Inc., Bethesda, MD, USA) algorithms. Figure 12
illustrates the process for a typical image. The image is registered to a background photo (cells
absent) and divided by the background to obtain a normalized image. The resulting image is
processed through a flattening algorithm to reduce illumination irregularities present throughout
the sequence and within individual frames (Fig. 12(c)).
To segment cells, we take advantage of the characteristics of phase contrast microscopy,
where cell pixels follow a bimodal intensity distribution. Protrusions (cell membrane
extensions) have lower intensities than the median, and therefore are segmented by selecting
pixels below a predefined intensity threshold (protrusion threshold). The contours of cell bodies
(cell bulk containing the nucleus) have higher intensities than the median, and therefore are
segmented by selecting pixels above a separate predefined intensity threshold (body threshold).
Segmented protrusions and cell bodies are found in Fig. 12(d-e), respectively. Extraneous debris
is identified using an area filter and removed. Figure 12(d) shows the resulting protrusions after
morphological dilation using an isotropic structuring element to minimize cell fragmentation.
The same morphological techniques are applied to the cell bodies in Fig. 12(e). The protrusion
and body images (Fig. 12(d-e)) are superimposed, and the result (Fig. 12(f)) is dilated to further
minimize fragmentation and then flood-filled to close gaps. Morphological erosion is applied to
8
shrink the dilated segments, followed by an additional debris filter. The resulting image is
overlaid on the flattened image to verify segmentation accuracy (Fig. 12(g)).
After segmentation, cells are selected for analysis, hand-corrected (if necessary), and tracked.
Hand correction is applied to under-detected cells by manual placement of 4-10 sided polygons
(Fig. 12(h)). Corrections apply to undetected protrusions and gaps in segmentation. The
sequence is then tracked using the semi-automatic tracking algorithm in Image-Pro. The
algorithm calculates trajectories for cell centroids as well as numerous morphological readouts.
Data are then compiled for statistical analysis. Cells that make contact with other cells (or
walls), divide, undergo apoptosis, or fail to attach are excluded from analysis (roughly 20-40%
of cells in each well).
Data are derived from 3 replicate experiments (3 devices) with 6 chambers per device.
Migrational and morphological data are collected from a total of 205 cells, which generate 243
cell tracks. First, the chemotactic index (CI) of cells for the entire region of interest (ROI) for
each experiment is calculated (see ROI in Fig. 6(a), main article). Then, the ROI is divided into
4 spatial sections, and each data point for CI, speed, area, and circularity is calculated from nonoverlapping subsequences of 7 consecutive photo frames, and each data point is binned into one
of the 4 sections in the chamber (Fig. 6(c), main article, and Fig. 13, Suppl. Material). The
chamber could potentially be divided into more or fewer sections depending on whether there are
enough cells (and corresponding tracks) in each section to produce results with meaningful
statistics. Area and circularity are calculated as the average from each set of 7 photos, and speed
is calculated by dividing the root-mean-square displacement by the time interval spanning the 7
photos (18 min). CI is defined as
CI 
d grad
,
(3)
d accum
where dgrad is the net displacement in the direction toward the gradient source (x-dimension) and
daccum is the accumulated distance traveled over the 7 photo set. Circularity is defined as
circularit y 
4A ,
p2
(4)
where A is cell area and p is cell perimeter.25
All statistical analyses are performed by ANOVA using Prism software (GraphPad Software
Inc., La Jolla, CA, USA). Tukey’s posthoc tests are performed.
9
FIG. 12. Cell segmentation. (a) Representative phase contrast image, prior to cell segmentation, with applicable region of
interest (ROI) (light gray border). (b-i) Magnified insets for clarity. (b) Original phase contrast image. (c) Background divided
and flattened image. (d) Segmented protrusions, followed by dilation. (e) Segmented cell body contours, followed by dilation.
(f) Superimposition of (d) and (e), followed by dilation and flood-fill operations. (g) Completed segmentations as a result of
debris filter and erosion operations. (h) Segmented objects overlaid on flattened image from (c); slight under-detection denoted
by arrow. (i) Hand-correction of under-detection. (j) Full image of segmented well. Scale: ROI rectangle is 1000 m in xdirection.
10
SPEED, AREA, AND CIRCULARITY RESULTS FROM CELL EXPERIMENTS
FIG. 13. Speed, area, and circularity from cell experiments by section. Results are shown by spatial section (A-D) for both
conditions (stage 1 and stage 2). Change of means is shown on the right. Experimental conditions the same as described in
Materials and Methods. Error bars are SEM.
11
FIG. 14. Control experiments are compared to stage 1 (the non-gradient stage) of gradient trials; no significant differences are
measured between conditions in any of the 4 sections (all pairwise tests yield p>0.05).
NUTRIENT TRANSPORT MODELS
To assess whether gradients could be formed in addition to the device-applied gradient, we
model the transport of glucose and oxygen based on the consumption rates of these nutrients by
cells using COMSOL finite element modeling (Multiphysics 4.2a, COMSOL AB, Stockholm,
Sweden). Results are presented in Fig. 15, showing 2-D representations of the lengthwisevertical cross-section of the chamber at its centerline. Although a 3-D model would be more
accurate, a 2-D model is considered adequate, since the width of the chamber (into the page) is
roughly 10× the height. Discrepancies due to the 3-D tapering geometry near the side of the
chamber and reduced flux area where wrap-around flow occurs could be compensated by
increasing effective consumption rate in the 2-D model. To this end, a sensitivity analysis with
respect to reaction rates is performed to account for any discrepancies.
In the models, a symmetry condition is applied so that the left edge represents the center of
the chamber. Constant boundary concentrations for glucose and oxygen are applied at the right
edge. Additionally, diffusion coefficients of glucose26 (Dglucose-water, 0.6×10-5 cm2/s) and
12
oxygen27 (Doxygen-water, 2.1×10-5 cm2/s) are approximated by their diffusion coefficients in water.
Furthermore, the diffusion coefficient of oxygen in PDMS28 (Doxygen-PDMS) was 5.2×10-6 cm2/s.
For glucose (Fig. 15(a)), a glucose concentration of 5.56 mol/m3 (c0,glucose) for DMEM solution is
used at the right boundary.29 Likewise, the oxygen boundary concentration (Fig. 15(b)) is set at
0.2143 mol/m3 (c0,oxygen), the equilibrium concentration for oxygen in water at 37 ºC.
A thick PDMS subdomain (3.5 mm), representing the bulk of the device, is above the
chamber in contact with air at the top (not shown in figure). A flux boundary condition is
defined here to describe the equilibrium concentrations at the PDMS-air interface using a
partition coefficient value of 0.287 (KPDMS/air), which is consistent with previous.30 Likewise, a
flux condition describing the oxygen equilibrium at the PDMS-water interface is defined in a
similar manner, using a partition coefficient value of 10 (KPDMS/water).28 In contrast, a “no flux”
condition was defined for glucose at the PDMS-water interface, given its negligible diffusion
through PDMS.
The consumption rates of oxygen and glucose for experimental cell seeding density were
used to define boundary conditions at the base of the chamber, where cells are attached. The
glucose consumption rate is approximated by NIH 3T3 cells in DMEM solution at a value of
1.88×10-2 fmol/cell/min.29 We use an average experimental cell seeding density of 15 cells per
6×105 µm2 (chamber area at the base). This leads to a total glucose consumption rate of 4.77×103
fmol/s, or 7.95×10-9 fmol/µm2/s (Rglucose). Likewise, the oxygen consumption rate is
approximated by immortalized mammalian cell lines at a value of 10 fmol/cell/min.31 Assuming
the same seeding density, this value yields a total rate of 2.5 fmol/s, or 4.17×10-6 fmol/µm2/s
(Roxygen).
The model shows virtually no gradient (<0.01% spatial change) in the steady-state
concentration of glucose across the chamber (Fig. 15(a)). A sensitivity analysis is performed on
the consumption rate of glucose, and at ten times the reported consumption rate, still no glucose
gradient occurs (concentration values of 5.56 mol/m3 were determined at both the center and
edge in all scenarios). Figure 15(b) shows that for the reported oxygen consumption rate, only a
0.31% difference in concentration exists from the center to edge of the chamber (concentration
values ~0.2136 mol/m3 at the center and ~0.2145 mol/m3 at the edge), evaluated at 10 µm above
the chamber base, as this is nearer to the surface where the cells would reside. Again, a
sensitivity analysis is performed, and at ten times the reported consumption rate, only a 3.21%
difference exists between the chamber center and edge (concentration values of ~0.2074 mol/m3
and ~0.2145 mol/m3, respectively). Eukaryotic cells are known to respond to very small
gradients of chemoattractants (~2% change across the cell area);32 however, the gradients for
oxygen and glucose shown in Fig. 15 are significantly smaller and are therefore assumed to be
unlikely to provoke a gradient-dependent response to those molecules.
13
FIG. 15. Model results and boundary conditions for gradients due to glucose and oxygen consumption by cells. Dashed lines:
red line represents a symmetry boundary, orange line represents a reaction (consumption) boundary, blue line represents the flux
condition at the PDMS-medium interface, and purple line represents the “no flux” condition, and green line represents constant
concentration at the chamber edge, where replenishment occurs during pulsed flow. (a) Steady-state glucose concentration due,
accounting for consumption of glucose by cells, shows virtually no gradient across the chamber. The constant concentration at
the chamber edge (c0,glucose) is approximated to be 5.56 mol/m3 for DMEM solution. Consumption rate of glucose (Rglucose) is
approximated by the measured rate for NIH 3T3 cells. (b) Steady-state oxygen concentration accounting for consumption of
oxygen by cells, which shows a 0.3% change from middle to edge of chamber (effectively no gradient). The constant
concentration at the chamber edge (c0,oxygen) is approximated at 0.2143 mol/m3. Since oxygen diffuses through PDMS, its
equilibrium concentration at the PDMS-water interface is accounted for using a flux boundary condition and reported partition
coefficient. Additionally, there is a flux boundary at the PDMS-air interface (not shown). The consumption rate of oxygen
(Roxygen) was approximated by the rate for immortalized mammalian cell lines, 4.17x10 -6 fmol/µm2/s.
SUPPLEMENTAL MOVIE 1: IMAGE SEQUENCE FROM A PRELIMINARY CELL
EXPERIMENT
The image sequence from a representative device (Trial 42) and chamber (Well 3) are
assembled into Supplemental Movie 1. Stage 1 (no gradient) spans 6 hrs. Stage 2 (FBS gradient
with source on left side) spans 12 hrs (hour 6 to hour 18). Change in cell morphologies is
evident after FBS gradient is engaged. Similar sequences are collected for each chamber for
14
each device. Cells are segmented and tracked according to the process described earlier (image
processing, cell tracking, and data analysis section).
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